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dynamicslab
GitHub Repository: dynamicslab/databook_python
 Path: blob/master/CH04/CH04_SEC06_1_kFoldValidation.ipynb
597 views
Kernel: Python 3
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from sklearn import linear_model
from mpl_toolkits.mplot3d import Axes3D 


rcParams.update({'font.size': 18})
plt.rcParams['figure.figsize'] = [12, 12]


n = 100
L = 4
x = np.linspace(0,L,n)
f = np.power(x,2) # parabola with 100 data points

M = 21 # Polynomial degree
phi = np.zeros((n,M))
for j in range(M):
    phi[:,j] = np.power(x,j) # build matrix A
    
trials = np.array([2, 10, 100])

fig,axs = plt.subplots(3,3)

for j in range(len(trials)):
    trial = trials[j]
    E1 = np.zeros(trial)
    E2 = np.zeros(trial)
    E3 = np.zeros(trial)
    
    A1 = np.zeros((M,trial))
    A2 = np.zeros((M,trial))
    A3 = np.zeros((M,trial))

    
    for jj in range(trial):
        f = np.power(x,2) + 0.2*np.random.randn(n)
        a1 = np.linalg.pinv(np.copy(phi)) @ np.copy(f)
        f1 = phi @ a1
        E1[jj] = np.linalg.norm(f-f1,ord=2)/np.linalg.norm(f,ord=2)
        
        a2 = np.linalg.lstsq(np.copy(phi),np.copy(f),rcond=None)[0]
        f2 = phi @ a2
        E2[jj] = np.linalg.norm(f-f2,ord=2)/np.linalg.norm(f,ord=2)
        
#         regr3 = linear_model.ElasticNet(alpha=1.0, copy_X=True, l1_ratio=0.1, max_iter=10**5,random_state=0)
        regr3 = linear_model.Lasso(alpha=1)
        regr3.fit(phi, f)  
        a3 = regr3.coef_
        f3 = phi @ a3
        E3[jj] = np.linalg.norm(f-f3,ord=2)/np.linalg.norm(f,ord=2)
        
        A1[:,jj] = a1
        A2[:,jj] = a2
        A3[:,jj] = a3
        
    A1m = np.mean(A1,axis=1)
    A2m = np.mean(A2,axis=1)
    A3m = np.mean(A3,axis=1)
    
    Err = np.column_stack((E1,E2,E3))
    
    axs[0,j].bar(range(M),A1m)
    axs[1,j].bar(range(M),A2m)
    axs[2,j].bar(range(M),A3m)
    
plt.show()
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.386736074691015, tolerance: 0.2338364082456627 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.582254721552253, tolerance: 0.22970391087095018 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.49821693608336, tolerance: 0.23180138573541337 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.930527268790513, tolerance: 0.2347486809257047 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.69906847685288, tolerance: 0.23314474214359818 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.623116380645655, tolerance: 0.23277665203653533 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.955815922484355, tolerance: 0.23279328434423038 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.38587253286552, tolerance: 0.23329184738304723 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 34.420031181345976, tolerance: 0.23313207413478404 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.881186364733814, tolerance: 0.23131539194588477 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 34.70985186839599, tolerance: 0.2317956604993213 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.955211621299377, tolerance: 0.23226106348937994 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.685786672982502, tolerance: 0.2292990270061494 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.487769083059362, tolerance: 0.23217989739643746 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.801593452430808, tolerance: 0.22976453198413266 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.26525594574272, tolerance: 0.23377142742742696 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.94382204555086, tolerance: 0.23241285443149828 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.883584963257913, tolerance: 0.23435994947033864 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.560833491051305, tolerance: 0.23419163807674023 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.10298124603544, tolerance: 0.23350054119102578 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.75477507774152, tolerance: 0.23461764867216112 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.609220962392833, tolerance: 0.2353812281804645 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.003542292794226, tolerance: 0.23470425720185295 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 34.23501193932414, tolerance: 0.23165690503081487 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.678377589715385, tolerance: 0.23114988872512338 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 34.11145342089566, tolerance: 0.23643486781445094 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.35128581482142, tolerance: 0.23187050162990983 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.00828135049151, tolerance: 0.23128843704070673 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.73986507918654, tolerance: 0.2332794821560532 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.787262363512674, tolerance: 0.23253632965614313 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.071453101394354, tolerance: 0.23214135350874496 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.8202301374655, tolerance: 0.2300393963349105 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.467077838054735, tolerance: 0.23502305710140228 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.81667813795755, tolerance: 0.2320636804877328 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.88659250021499, tolerance: 0.23370191872002372 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 29.753695043173437, tolerance: 0.23085074006287287 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.24597629930734, tolerance: 0.23611915933046776 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.219440763049732, tolerance: 0.23183836202377384 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.12054324433148, tolerance: 0.23341571870784503 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.381181642353503, tolerance: 0.23114478266823527 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.228227447968386, tolerance: 0.23039465932000164 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.33025441033081, tolerance: 0.228885109281057 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.86111483318495, tolerance: 0.23160600551797547 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.64428730087602, tolerance: 0.23396682266871505 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.254717387929922, tolerance: 0.2324826398798131 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.934536474402808, tolerance: 0.23018635197722717 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.684144930124873, tolerance: 0.22991981229904568 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.28661901800622, tolerance: 0.23073338338309027 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 29.720550501318392, tolerance: 0.23121641340399238 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.786000334443433, tolerance: 0.23064848096607307 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.342125572204658, tolerance: 0.23347261684970497 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 29.795243936767392, tolerance: 0.23260500421730096 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.736247377361593, tolerance: 0.2342362640354149 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.001198940362194, tolerance: 0.23223096834190193 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.363614800350646, tolerance: 0.22975059914885065 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.07249129270395, tolerance: 0.2342548099488493 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.56949090114297, tolerance: 0.23191117891141882 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.277388287280118, tolerance: 0.22825337341411006 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.00352631814355, tolerance: 0.23336644847178178 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.96702956237427, tolerance: 0.23511057337160457 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.60926083740771, tolerance: 0.23491148471607154 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.32447039498819, tolerance: 0.23265473548952284 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.52188247653253, tolerance: 0.22954580596835733 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.344100825208955, tolerance: 0.23336930102253964 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.64220623082805, tolerance: 0.23525069312904995 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.42731597352406, tolerance: 0.23365637206660145 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.494357803398763, tolerance: 0.23700370654282799 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.573828507416266, tolerance: 0.23280027805960654 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.29039978450121, tolerance: 0.23509621278272153 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.822825261562237, tolerance: 0.2303481544175588 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.426022667960936, tolerance: 0.23157528128628393 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.893823433922073, tolerance: 0.23352443492162853 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.79545689814503, tolerance: 0.23359581249990022 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.02947638383185, tolerance: 0.22941403342597483 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.1191096852244, tolerance: 0.23371826568644785 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.33459943974062, tolerance: 0.23361446059598126 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.500666132494707, tolerance: 0.23369653073259516 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.023369649636976, tolerance: 0.23345662022860633 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.32532259584102, tolerance: 0.23519595063125637 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.068210436831166, tolerance: 0.23006128008541166 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.534764558691805, tolerance: 0.23344121305404658 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.927568340580578, tolerance: 0.2310261354937974 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.03511962859397, tolerance: 0.2347211697590382 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.792814533726386, tolerance: 0.23093170261948373 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 34.29253928199928, tolerance: 0.23587699795349082 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.91349189664362, tolerance: 0.23211969597095092 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.894330773722395, tolerance: 0.2326908775056565 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.84137333146917, tolerance: 0.23605406738411916 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.509447766531913, tolerance: 0.23348348332195684 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.799046715698218, tolerance: 0.23236735430499814 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.584022737882535, tolerance: 0.23235996472270673 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.764855069756308, tolerance: 0.22964683352072918 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.626221873861674, tolerance: 0.23365457408929644 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 29.77663060577052, tolerance: 0.2347079538518311 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.22909857888215, tolerance: 0.22994618477620876 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.73596699965796, tolerance: 0.23537823711747757 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.575202171011256, tolerance: 0.23357952832216558 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.61863812396522, tolerance: 0.23532560373752096 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 30.638817620909023, tolerance: 0.23256998204018742 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.23773969020388, tolerance: 0.22958145662842736 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.822864761010877, tolerance: 0.23187215022150642 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.459833386825792, tolerance: 0.23131613999762604 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.9272142463483, tolerance: 0.23310542740122533 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.071752698746288, tolerance: 0.22982081616569563 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.1570357542048, tolerance: 0.2306291449920942 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.519303563678953, tolerance: 0.2312608198482505 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.576940601396036, tolerance: 0.2322938594217306 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.56892359421117, tolerance: 0.23039854393196862 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.042595734354165, tolerance: 0.23970627958952848 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 32.130382294154295, tolerance: 0.23417664028416604 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 33.53128645944835, tolerance: 0.2305578145409616 positive) C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 31.802138769422562, tolerance: 0.23403655690659425 positive)
Image in a Jupyter notebook
plt.rcParams['figure.figsize'] = [8,8]

Atot = np.column_stack((A1m,A2m,A3m)) # Average loadings of three methods
Atot2 = (Atot>0.2) * Atot # threshold
Atot3 = np.column_stack((Atot,Atot2)) # combine both thresholded and not

for j in range(3):
    plt.bar(np.arange(Atot.shape[0])*4+j,Atot[:,j],label='A'+str(j+1)+'m')
    
plt.xlim(0,4*M)
plt.title('Unthresholded')
plt.legend()

plt.figure()
for j in range(3):
    plt.bar(np.arange(Atot2.shape[0])*8+j,Atot[:,j],label='A'+str(j+1)+'m')
    
plt.title('Thresholded')
plt.xlim(0,4*M)
plt.legend()

plt.show()
Image in a Jupyter notebookImage in a Jupyter notebook
n = 200
L = 8
x = np.linspace(0,L,n)
x1 = x[:100]    # Train
x2 = x[100:200] # Test
n1 = len(x1)
n2 = len(x2)
ftrain = np.power(x1,2) # Train parabola x = [0,4]
ftest = np.power(x2,2)  # Test parabola x = [4,8]

phi_i = np.zeros((n1,M))
phi_e = np.zeros((n2,M))

for j in range(M):
    phi_i[:,j] = np.power(x1,j) # interpolation key
    phi_e[:,j] = np.power(x2,j) # extrapolation key
    
Eni = np.zeros(6)
Ene = np.zeros(6)
for jj in range(6): # compute inter/extra-polation scores
    ani = Atot3[:,jj]
    fnai = phi_i @ ani
    Eni[jj] = np.linalg.norm(ftrain-fnai,ord=2)/np.linalg.norm(ftrain,ord=2)
    fnae = phi_e @ ani
    Ene[jj] = np.linalg.norm(ftest-fnae,ord=2)/np.linalg.norm(ftest,ord=2)
    
fig,axs = plt.subplots(2,2)
axs[0,0].bar(range(6),Eni)
axs[0,1].bar(range(6),Ene)
axs[1,0].bar(range(6),Eni)
axs[1,0].set_xlim(-0.5,6.5)
axs[1,0].set_ylim(0,0.01)
axs[1,1].bar(range(6),Ene)
axs[1,1].set_xlim(-0.5,6.5)
axs[1,1].set_ylim(0,0.1)

plt.show()
Image in a Jupyter notebook